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In a certain year, the difference between Mary's and Jim's
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Updated on: 04 Mar 2013, 03:38

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55% (01:52) correct 45% (01:59) wrong based on 1745 sessions

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In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year. (2) Kate's annual salary was $40,000 that year.

Re: In a certain year, the difference between Mary's and Jim's
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30 Aug 2016, 06:52

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5

alimad wrote:

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year. (2) Kate's annual salary was $40,000 that year.

Let's first deal with the given information. Let J = Jim's salary Let M = Mary's salary Let K = Kate's salary

Notice that the salaries (in ascending order) must be J, K, M Also, if the difference between Mary's and Jim's annual salaries equals twice the difference between Mary's and Kate's annual salaries, then we can conclude that the 3 salaries are equally spaced.

Target question: What was the average annual salary of the 3 people that year?

Statement 1: Jim's annual salary was $30,000 that year. In other words, J = 30,000 So, the three salaries, arranged in ascending order are: 30,000, K, M Plus we know that the 3 salaries are equally spaced. Do we now have enough information to answer the target question? No.

For proof that that we don't have enough information, consider these 2 cases: Case a: J=30,000, K=30,001, M=30,002, in which case the average salary is $30,001 Case b: J=30,000, K=30,002, M=30,004, in which case the average salary is $30,002 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Kate's annual salary was $40,000 that year. In other words, K = 40,000 Perfect! Since the 3 salaries are equally spaced, we can use a nice rule that says, "If the numbers in a set are equally spaced, then the mean and median of that set are equal" Since Kate's salary must be the median salary, we now know that the average salary must be $40,000 Since we can answer the target question with certainty, statement 2 is SUFFICIENT

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kat's annual salaries. If Mary's annual salry was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

Jim's annual salary was $30,000 that year Kate's annual salary was $40,000 that year

In a certain year, the difference between Mary's and Jim's annual salary was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary is the highest of the three people, what was the average (arithmetic mean) annual salary of the 3 people last year?

1) Jim's annual salary was $30,000 that year 2) Kate's annual salary was $40,000 that year.

Clearly IMO B

consider the given condition=>say mary's sal =m,ken's=k,jim's=j then given that => m-j = 2(m-k) =>m+j=2k now consider Question m+j+k) /3 =? that is 3k/3=k =? hence knowig k is sufficient to answr but knowing j is not suffi.hence (1) is not suffi and (2) is sufficient hence IMO B
_________________

Concentration: Entrepreneurship, International Business

GMAT 1: 730 Q50 V39

GPA: 3.2

WE: Education (Education)

Re: In a certain year, the difference between Mary's and Jim's
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01 Mar 2013, 12:50

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5

Let me try too clarify this one for you.

Let Mary's, Jim's and Kate's salaries be M,J and K respectively. The question states that

(M-J)=2(M-K). This implies that -J=M-2K ==>M+J=2K We also know that Mary's salary was the highest among the three people. We need to find (M+K+J)/3=3K/3=K Hence, all we need is Kate's Salary.

Now let us consider statement 1. It tells is about Jim's salary. However, we still do not know the difference between Mary's and Jim's salaries or Mary's salary. So, we cannot go further with this calculations. INSUFFICIENT

Let us consider statement 2. This gives us exactly what we want, so this is SUFFICIENT.

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kat's annual salaries. If Mary's annual salry was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

Jim's annual salary was $30,000 that year Kate's annual salary was $40,000 that year

This approach takes a long time. Please provide an alternative solution. Thanks

Woah, slow down there killer. Thats too much work!

equation from stem: M-J=2(M-K) --> M-K=2M-2K --> M=2K-J

We want to know (M+J+K)/3

2K-J+J+K --> 3K/3 --> K is the average. If we know K then Suff.

So B is the answer.

Make sure to double check though to see if we can't get any others similar to 3K/3. ex/ maybe we can get 3J/3 or 4J/3 and so on... turns out we can't.

I think your rationale is good, however just wanted to know something. When they mention the difference between Mark, Jane, etc. Don't we need to put it in Absolute Value?

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kat's annual salaries. If Mary's annual salry was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

Jim's annual salary was $30,000 that year Kate's annual salary was $40,000 that year

This approach takes a long time. Please provide an alternative solution. Thanks

Woah, slow down there killer. Thats too much work!

equation from stem: M-J=2(M-K) --> M-K=2M-2K --> M=2K-J

We want to know (M+J+K)/3

2K-J+J+K --> 3K/3 --> K is the average. If we know K then Suff.

So B is the answer.

Make sure to double check though to see if we can't get any others similar to 3K/3. ex/ maybe we can get 3J/3 or 4J/3 and so on... turns out we can't.

I think your rationale is good, however just wanted to know something. When they mention the difference between Mark, Jane, etc. Don't we need to put it in Absolute Value?

Cheers J

Notice that we are told that "Mary's annual salary was the highest of the 3 people", thus |M-J|=M-J and |M-K|=M-k, so no need of modulus here.
_________________

We know that: A) the order is Mary --> Kate --> Jim B) the difference between Mary and Kate is twice the difference between Mary and Jim - this is an arithmetic progression with 3 integers.

For statements: 1) We know Jim's annual salary but not the difference - meaning we do not know Kate or Mary's annual salary. We cannot find the average. (not sufficient)

2) We know Kate's annual salary. For an arithmetic progression of an odd number of integers, the average is the the middle integer. Kate's salary is the average. (sufficient)

What do you think?

Bunuel wrote:

jlgdr wrote:

GMATBLACKBELT wrote:

Woah, slow down there killer. Thats too much work!

equation from stem: M-J=2(M-K) --> M-K=2M-2K --> M=2K-J

We want to know (M+J+K)/3

2K-J+J+K --> 3K/3 --> K is the average. If we know K then Suff.

So B is the answer.

Make sure to double check though to see if we can't get any others similar to 3K/3. ex/ maybe we can get 3J/3 or 4J/3 and so on... turns out we can't.

I think your rationale is good, however just wanted to know something. When they mention the difference between Mark, Jane, etc. Don't we need to put it in Absolute Value?

Cheers J

Notice that we are told that "Mary's annual salary was the highest of the 3 people", thus |M-J|=M-J and |M-K|=M-k, so no need of modulus here.

We know that: A) the order is Mary --> Kate --> Jim B) the difference between Mary and Kate is twice the difference between Mary and Jim - this is an arithmetic progression with 3 integers.

For statements: 1) We know Jim's annual salary but not the difference - meaning we do not know Kate or Mary's annual salary. We cannot find the average. (not sufficient)

2) We know Kate's annual salary. For an arithmetic progression of an odd number of integers, the average is the the middle integer. Kate's salary is the average. (sufficient)

What do you think?

Bunuel wrote:

Notice that we are told that "Mary's annual salary was the highest of the 3 people", thus |M-J|=M-J and |M-K|=M-k, so no need of modulus here.

Re: In a certain year, the difference between Mary's and Jim's
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30 Nov 2014, 22:48

I agree of all your opinion. But how do you think about my approach?

We can think that the ratio of Mary:Kate:Jim is 5a:4a:1a, because the difference of Mary and Jim is twice of that of Mary and Kate. Then the answer could be 'D'.

Re: In a certain year, the difference between Mary's and Jim's
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01 Dec 2014, 03:03

AnthonySS wrote:

I agree of all your opinion. But how do you think about my approach?

We can think that the ratio of Mary:Kate:Jim is 5a:4a:1a, because the difference of Mary and Jim is twice of that of Mary and Kate. Then the answer could be 'D'.

How do you get this ratio?

m - j = 2 (m -k) m - j = 2m - 2k 2k = m + j

We cannot get the ratio m:k:j from 2k = m + j.
_________________

Re: In a certain year, the difference between Mary's and Jim's
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01 Dec 2014, 19:06

Bunuel wrote:

AnthonySS wrote:

I agree of all your opinion. But how do you think about my approach?

We can think that the ratio of Mary:Kate:Jim is 5a:4a:1a, because the difference of Mary and Jim is twice of that of Mary and Kate. Then the answer could be 'D'.

Re: In a certain year, the difference between Mary's and Jim's
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01 Dec 2014, 23:37

AnthonySS wrote:

Bunuel wrote:

AnthonySS wrote:

I agree of all your opinion. But how do you think about my approach?

We can think that the ratio of Mary:Kate:Jim is 5a:4a:1a, because the difference of Mary and Jim is twice of that of Mary and Kate. Then the answer could be 'D'.

Re: In a certain year, the difference between Mary's and Jim's
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15 Feb 2015, 01:56

1

With DS problems, I like to start by figuring out as much info as possible from the prompt. So, we know that M-J=2(M-K) which we can simplify to M=2K-J

(because we know that Mary has the highest salary. We also know that M>K>J because the difference between mary and jim is bigger

We are looking for the average, so if we can figure out the sum (M+J+K), which we can substitute in the new M and get 2K-J+K+J, or 3K so basically, all we need is J and we know the average.

(I) tells us that J=30,000, which doesn't really help us (II) gives us K, which is 40,000, so we know the sum is 120,000 and the average is 40,000
_________________

Re: In a certain year, the difference between Mary's and Jim's
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02 Mar 2015, 02:21

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year. (2) Kate's annual salary was $40,000 that year.

Re: In a certain year, the difference between Mary's and Jim's
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02 Mar 2015, 02:37

ssriva2 wrote:

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year. (2) Kate's annual salary was $40,000 that year.